U.S. patent number 3,984,834 [Application Number 05/571,154] was granted by the patent office on 1976-10-05 for diagonally fed electric microstrip dipole antenna.
This patent grant is currently assigned to The Unites States of America as represented by the Secretary of the Navy. Invention is credited to Cyril M. Kaloi.
United States Patent |
3,984,834 |
Kaloi |
October 5, 1976 |
**Please see images for:
( Certificate of Correction ) ** |
Diagonally fed electric microstrip dipole antenna
Abstract
A diagonally fed electric microstrip dipole antenna consisting
of a thin ctrically conducting, rectangular-shaped element formed
on one surface of a dielectric substrate, the ground plane being on
the opposite surface. The length of the element determines the
resonant frequency. The feed point is located along the diagonal
with respect to the antenna length and width, and the input
impedance can be varied to match any source impedance by moving the
feed point along the diagonal line of the antenna without affecting
the radiation pattern. The antenna bandwidth increases with the
width of the element and spacing between the element and ground
plane. Singularly fed circular polarization is easily obtained with
this antenna.
Inventors: |
Kaloi; Cyril M. (Thousand Oaks,
CA) |
Assignee: |
The Unites States of America as
represented by the Secretary of the Navy (Washington,
DC)
|
Family
ID: |
24282521 |
Appl.
No.: |
05/571,154 |
Filed: |
April 24, 1975 |
Current U.S.
Class: |
343/700MS;
343/830 |
Current CPC
Class: |
H01Q
9/0407 (20130101) |
Current International
Class: |
H01Q
9/04 (20060101); H01A 009/28 (); H01A 001/38 () |
Field of
Search: |
;343/846,7MS,830 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Lieberman; Eli
Attorney, Agent or Firm: Sciascia; Richard S. St. Amand;
Joseph M.
Claims
I claim:
1. A diagonally fed electric microstrip dipole antenna having low
physical profile and conformal arraying capability, comprising:
a. A thin ground plane conductor;
b. a thin rectangular radiating element for producing a radiation
pattern being spaced from said ground plane;
c. said radiating element being electrically separated from said
ground plane by a dielectric substrate;
d. said radiating element being fed at a single feed point located
along a diagonal line of the element;
e. said radiating element being fed from a single coaxial to
microstrip adapter, the center pin of said adapter extending
through said ground plane and dielectric substrate to said
radiating element;
f. the length of said radiating element determining the resonant
frequency of said antenna;
g. the antenna input impedance being variable to match most
practical impedances as said feed point is moved along said
diagonal line;
h. the antenna bandwidth being variable with the width of the
radiating element and the spacing between said radiating element
and said ground plane, said spacing between the radiating element
and the ground plane having somewhat greater effect on the
bandwidth than the element width;
i. said radiating element being operable to oscillate in two modes
of current oscillation, each of said two modes being orthogonal to
the other and the mutual coupling being minimal, the properties of
each mode of oscillation being determined independently of each
other; the parallel combination of the input impedance of each mode
providing a combined antenna input impedance;
j. antenna polarization being linear when the radiating element
length and width are equal, and the antenna polarization being
circular when the phase difference between the two modes of
oscillation are in quadrature due to differences between the length
and width of the antenna.
2. An antenna as in claim 1 wherein the ground plane conductor
extends at least one wavelength beyond each edge of said radiating
element to minimize any possible backlobe radiation.
3. An antenna as in claim 1 wherein said thin rectangular radiation
element is in the form of a square and the polarization is linear
along the diagonal on which the feed point lies.
4. An antenna as in claim 1 wherein a plurality of said radiating
elements are arrayed to provide a near isotropic radiation
pattern.
5. An antenna as in claim 1 wherein the length of said radiating
element is approximately 1/2 wavelength.
6. An antenna as in claim 1 wherein said antenna radiation pattern
can be vaied from diagonal fields to circulating fields depending
upon the input impedance of each of said two modes of current
oscillation.
7. An antenna as in claim 1 wherein said thin radiating element is
formed on one surface of said dielectric substrate.
8. An antenna as in claim 1 wherein the radiation pattern of said
antenna is operable to be circularly polarized by advancing one
mode of current oscillation and retarding the other mode of current
oscillation until there is a 90.degree. phase difference, and by
coupling the same amount of power into each mode of
oscillation.
9. An antenna as in claim 1 wherein the length of the antenna
radiating element is determined using Newton's Method of successive
approximation by the equation:
where
A is the length to be determined
F = the center frequency (Hz)
H = the thickness of the dielectric
.epsilon. = the dielectric constant of the substrate.
10. An antenna as in claim 1 wherein the radiation patterns for
each mode of oscillation ae power patterns,
.vertline.E.sub..theta..vertline..sup.2 and
.vertline.E.sub..phi..vertline..sup.2, plarization field
E.sub..phi. and the field normal to the polarization field
E.sub..theta., and are given by the equations: ##EQU40## and
##EQU41## where U = (U2-U3)/U5
T = (t3-t4/t8
u2 = p sin (A .times. P/2) cos (k .times. A .times. sin .theta. sin
.phi./2)
U3 = k sin .theta. and .phi. cos (A .times. P/2) sin (k .times. A
.times. sin .theta. sin .phi./2)
U5 = (p.sup.2 - k.sup.2 sin.sup. 2 .theta. sin.sup. 2 .phi.)
T3 = p sin (P .times. B/2) cos (k .times. B .times. cos
.theta./2)
T4 = k cos .theta. cos (P .times. B/2) sin k .times. B .times. cos
.theta./2)
T8 = (p.sup.2 - k.sup.2 cos.sup.2 .theta.)
I.sub.m = maximum current (amps) ##EQU42## .lambda. = free space
wave length (inches) .lambda..sub.g = waveguide wavelength (inches)
and .lambda..sub.g = 2 .times. A + (4 .times. H
.sqroot..epsilon.)
r = the range between the antenna and an arbitrary point in space
(inches)
Z.sub.o = characteristic impedance of the element (ohms)
and Z.sub.o is given by ##EQU43## H = the thickness of the
dielectric B = the width of the antenna element
.epsilon. = the dielectric constant of the substrate (no
units).
11. An antenna as in claim 1 wherein the minimum width of said
radiating element is determined by the equivalent internal
resistance of the conductor plus any loss due the dielectric.
12. An antenna as in claim 1 wherein the input impedance, R.sub.in,
is given by the equation ##EQU44## where R.sub.a the radiation
resistance
2R.sub.c = the total internal resistance
Z.sub.o = characteristic impedance of the element, and
y.sub.o = distance of feed point from the center of the
element.
13. An antenna as in claim 1 wherein only a slight difference
exists between the element length and width from being of equal
dimension and the polarization is circular; the amount said
radiating element length is increased from the equal dimension is
determined by the equation ##EQU45## and the amount said radiating
element width is decreased from the equal dimension is determined
by the equation ##EQU46## where: .alpha..sub.A and .alpha..sub.B
are propagation constants for the antenna circuit,
l.sub.A is the length of the antenna radiating element,
l.sub.B is the width of the antenna radiating element,
.lambda.g is the waveguide wavelength.
14. An antenna as in claim 1 wherein a slight change in the element
length and width from being of equal dimension up to approximately
0.5% difference will result in changes in some antenna
characteristics and cause the polarization to change from linear
along the diagonal to near circular polarization.
15. An antenna as in claim 1 wherein each of the two modes of
oscillation have the same properties and one-half of the available
power is coupled to one mode of oscillation and one-half if the
available power is coupled to the other mode of oscillation.
Description
This invention is related to copending U.S. Pat. applications:
Ser. No. 571,157 for OFFSET FED MICROSTRIP DIPOLE ANTENNA;
Ser. No. 571,156 for END FED MICROSTRIP QUADRUPOLE ANTENNA;
Ser. No. 571,155 for COUPLED FED MICROSTRIP DIPOLE ANTENNA;
Ser. No. 571,152 for CORNER FED MICROSTRIP DIPOLE ANTENNA;
Ser. No. 571,153 for NOTCH FED MICROSTRIP DIPOLE ANTENNA; and
Ser. No. 571,158 for ASYMMETRICALLY FED ELECTRIC MICROSTRIP DIPOLE
ANTENNA; all filed together herewith on Apr. 24, 1975 by Cyril M.
Kaloi.
BACKGROUND OF THE INVENTION
This invention relates to antennas and more particularly to a low
physical profile antenna that can be arrayed to provide near
isotropic radiation patterns.
In the past, numerous attempts have been made using stripline
antennas to provide an antenna having ruggedness, low physical
profile, simplicity, low cost, and conformal arraying capability.
However, problems in reproducibility and prohibitive expense made
the use of such antennas undesirable. Older type antennas could not
be flush mounted on a missle or airfoil surface. Slot type antennas
required more cavity space, and standard dipole or monopole
antennas could not be flush mounted.
SUMMARY OF THE INVENTION
The present antenna is one of a family of new microstrip antennas
and uses a very thin laminated structure which can readily be
mounted on flat or curved, irregular structures, presenting low
physical profile where minimum aerodynamic drag is required. The
specific type of microstrip antenna described herein is the
diagonally fed electric microstrip dipole. This antenna can be
arrayed with interconnecting coaxial feedlines to each of the
elements. The antenna elements can be photo-etched simultaneously
on a dielectric substrate. Using this technique, one
coaxial-to-microstrip adapter for each element is required to
interconnect an array of these antennas with a transmitter or
receiver since the feedpoints to the elements are along a diagonal
and inside the edges of the elements. Circular polarization is
obtainable in a single diagonally fed element with the use of a
single coaxial-to-microstrip adapter and no phase shifters.
Reference is made to the electric microstrip dipole instead of
simply the microstrip dipole to differentiate between two basic
types; the first being the electric microstrip type, and the second
being the magnetic microstrip type. The diagonally fed electric
microstrip dipole antenna belongs to the electric microstrip type
antenna. The electric microstrip antenna consists essentially of a
conducting strip called the radiating element and a conducting
ground plane separated by a dielectric substrate. The length of the
radiating element is approximately 1/2 wavelength. The width may be
varied depending on the desired electrical characteristics. The
conducting ground plane is usually much greater in length and width
than the radiating element.
The magnetic microstrip antenna's physical properties are
essentially the same as the electric microstrip antenna, except the
radiating element is approximately 1/4 the wavelength and also one
end of the element is grounded to the ground plane.
The thickness of the dielectric substrate in both the electric and
magnetic microstrip antenna should be much less than 1/4 the
wavelength. For thickness approaching 1/4 the wavelength, the
antenna radiates in a monopole mode in addition to radiating in a
microstrip mode.
The antenna as hereinafter described can be used in missiles,
aircraft and other type applications where a low physical profile
antenna is desired. The present type of antenna element provides
completely different radiation patterns and can be arrayed to
provide near isotropic radiation patterns for telemetry, radar,
beacons, tracking, etc. By arraying the present antenna with
several elements, more flexibility in forming radiation patterns is
permitted. In addition, the antenna can be designed for any desired
frequency within a limited bandwidth, preferably below 25 GHz,
since the antenna will tend to operate in a hybrid mode (e.g., a
microstrip/monopole mode) above 25 GHz for most commonly used
stripline materials. However, for clad materials thinner than 0.031
inch, higher frequencies can be used. The design technique used for
this antenna provides an antenna with ruggedness, simplicity, low
cost, a low physical profile, and conformal arraying capability
about the body of a missile or vehicle where used including
irregular surfaces while giving excellent radiation coverage. The
antenna can be arrayed over an exterior surface without protruding,
and be thin enough not to affect the airfoil or body design of the
vehicle. The thickness of the present antenna can be held to an
extreme minimum depending upon the bandwidth requirement; antennas
as thin as 0.005 inch for frequencies above 1,000 MHz have been
successfully produced. Due to its conformability, this antenna can
be applied readily as a wrap around band to a missile body without
the need for drilling or injuring the body and without interfering
with the aerodynamic design of the missile. In the present type
antenna, it is not necessary to ground the antenna element to the
ground plane. Further, the antenna can be easily matched to most
practical impedances by varying the location of the feed point
along the diagonal of the element.
Advantages of the antenna of this invention over other similar
appearing types of microstrip antennas is that the present antenna
can be fed very easily from the ground plane side and has a
slightly wider bandwidth for the same form factor.
The diagonally fed electric microstrip dipole antenna consists of a
thin, electrically-conducting, rectangular-shaped element formed on
the surface of a dielectric substrate; the ground plane is on the
opposite surface of the dielectric substrate and the microstrip
antenna element is fed from a coaxial-to-microstrip adapter, with
the center pin of the adapter extending through the ground plane
and dielectric substrate to the antenna element. The feed point is
located along the diagonal line of the antenna element. While the
input impedance will vary as the feed point is moved along the
diagonal line of the antenna element, the radiation pattern will
not be affected by moving the feed point. This antenna can be
easily matched to most practical impedances by varying the location
of the feed point along the diagonal of the element. Also,
singularly fed circular polarization can easily be obtained with
this diagonally fed antenna. The antenna bandwidth increases with
the width of the element and the spacing (i.e., thickness of
dielectric) between the ground plane and the element; the spacing
has a somewhat greater effect on the bandwidth than the element
width. The radiation pattern changes very little within the
bandwidth of operation for the linear polarization
configuration.
Design equations sufficiently accurate to specify the important
design properties of the diagonally fed electric dipole antenna are
also included below. These design properties are the input
impedance, the gain, the bandwidth, the efficiency, the
polarization, the radiation pattern, and the antenna element
dimensions as a function of the frequency. The design equations for
this type antenna and the antennas themselves are new.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates the alignment coordinate system used for the
diagonally fed electric microstrip dipole antenna.
FIG. 2A is an isometric planar view of a typical diagonally fed
electric microstrip dipole antenna.
FIG. 2B is a cross-sectional view taken along section line B--B of
FIG. 2A.
FIG. 3 is a plot showing the return loss versus frequency for the
diagonally fed antenna having the dimensions shown in FIGS. 2A and
2B.
FIGS. 4 and 5 show the antenna radiation patterns (XY-Plane plot)
of E.sub..phi. field and E.sub..theta. field polarization,
respectively, for the antenna shown in FIGS. 2A and 2B.
FIGS. 6 and 7 show the antenna radiation patterns for both
diagonals for the antenna shown in FIGS. 2A and 2B.
FIG. 8A is an isometric planar view of a typical singularly fed,
circularly polarized, electric microstrip dipole antenna.
FIG. 8B is a cross-sectional view taken along section line B--B of
FIG. 2A.
FIG. 9 is a plot showing the return loss versus frequency for a
circularly polarized antenna having the dimensions as shown in
FIGS. 8A and 8B.
FIGS. 10 and 11 show antenna radiation patterns (XY-Plane plot) at
2185 MHz for the circularly fed antenna shown in FIGS. 8A and
8B.
FIGS. 12 and 13 show antenna radiation patterns along both
diagonals at 2185 MHz for the circularly fed antenna shown in FIGS.
8A and 8B.
FIGS. 14 and 15 show antenna radiation patterns (XY-Plane plot) at
2217 MHz for the circularly fed antenna shown in FIGS. 8A and
8B.
FIGS. 16 and 17 show radiation plots along both diagonals at 2217
MHz for the circularly fed antenna shown in FIGS. 8A and 8B.
FIG. 18 illustrates the general configuration of the near field
radiation when fed along the diagonal of the antenna as in FIGS. 2A
and 2B.
FIG. 19 shows the alignment coordinate system with a hypothetical
feed point located beyond the corner of the element for the purpose
of discussing circular polarization.
DESCRIPTION AND OPERATION
The coordinate system used and the alignment of the antenna element
within this coordinate system are shown in FIG. 1. The coordinate
system is in accordance with the IRIG (Inter-Range Instrumentation
Group) Standards and the alignment of the antenna element was made
to coincide with the actual antenna patterns that will be shown
later. The B dimension is the width of the antenna element. The A
dimension is the length of the antenna element. The H dimension is
the height of the antenna element above the ground plane and also
the thickness of the dielectric. The AG dimension and the BG
dimension are the length and the width of the ground plane,
respectively. The y.sub.o dimension is the location of the feed
point measured from the center of the antenna element. The angles
.theta. and .phi. are measured per IRIG Standards. The above
parameters are measured in inches and degrees.
FIGS. 2A and 2B show a typical square diagonally fed electric
microstrip dipole antenna of the present invention. The typical
antenna is illustrated with the dimensions given in inches as shown
in FIGS. 2A and 2B, by way of example, and the curves shown in
later figures are for the typical antenna illustrated. The antenna
is fed from a coaxial-to-microstrip adapter 10, with the center pin
12 of the adapter extending through the dielectric substrate 14 and
to the feed point on microstrip element 16. The microstrip antenna
can be fed with most of the different types of
coaxial-to-microstrip launchers presently available. The dielectric
substrate 14 separates the element 16 or 17 from the ground plane
18 electrically.
As shown in FIG. 2A, the element 16 is fed on a diagonal with
respect to the A and B dimensions. The location of the y.sub.o
dimension along the A dimension is equal to the y.sub.o dimension
along the B dimension. The square element 16, when fed on a
diagonal, operates in a degenerate mode, i.e., two oscillation
modes occuring at the same frequency. These oscillations occur
along the Y axis and also along the Z axis. Dimension A determines
the resonant frequency along the Y axis and dimension B determines
the resonant frequency along the Z axis. Other parameters
contribute to a lesser degree to the resonant frequency. If the
element is a perfect square, the resonant frequencies are the same
and the phase difference between these two oscillations are zero.
For this case, the resultant radiated field vector is along the
diagonal and in line with the feed point, as shown later in FIG.
18. Mode degeneracy in a perfectly square element is not
detrimental. The only apparent change is that the polarization is
linear along the diagonal and in line with the feed point instead
of in line with the oscillations. All other properties of the
antenna remain as if oscillation is taking place in one mode only
and this is shown by FIGS. 3 through 7. FIG. 3 shows a plot of
return loss versus frequency for the square element of FIGS. 2A and
2B. FIGS. 4 and 5 show radiation plots for the XY plane with
E.sub..phi. field and E.sub..theta. field polarization at the
receiver antenna. The XZ plane plots were similar to the XY plane
plots, and therefore are not shown. FIGS. 6 and 7 show radiation
plots for both diagonals. Radiation cross-polarization plots in the
diagonal planes showed minimal energy, and therefore are not
shown.
Since the design equations for this type of antenna are new,
pertinent design equations that are sufficient to characterize this
type of antenna are therefore presented.
Design equations for the diagonally fed microstrip antenna are
subject to change with slight variation in the antenna element
dimension. This is particularly true with the antenna gain, antenna
radiation pattern, antenna bandwidth and the antenna polarization.
For this reason, the combined radiation fields are not presented.
It is much easier to understand the operation of the diagonally fed
antenna if the A mode of oscillation properties are presented first
and where applicable relate to the B mode of oscillation.
Before determining the design equations for the A mode of
oscillation, the following statements are given:
1. The A mode of oscillation and the B mode of oscillation are
orthogonal to one another and as such the mutual coupling is
minimum.
2. If both the A mode of oscillation and the B mode of oscillation
have the same properties, one-half of the available power is
coupled to the A mode and one-half is coupled to the B mode of
oscillation.
3. The combined input impedance is the parallel combination of the
impedance of the A mode of oscillation and the B mode of
oscillation.
4. Since the A mode of oscillation is orthogonal to the B mode of
oscillation, the properties of each mode of oscillation can be
determined independently of each other and a few of the combined
properties can be determined in the manner prescribed above.
5. It is emphasized again that only a slight change in the element
dimension will cause a large change in some of the antenna
properties. For example, it will be shown later that less than 0.5%
change in the element dimension can cause the polarization to
change from linear along the diagonal to near circular.
DESIGN EQUATIONS
The design equations will be obtained for the A mode of
oscillation. In most cases, the equations obtained for the A mode
of oscillation apply also to the B mode of oscillation since the A
dimension is assumed to be equal to the B dimension.
ANTENNA ELEMENT DIMENSION
The equation for determining the length of the antenna element when
A = B is given by
where
x = indicates multiplication
F = center frequency (Hz)
.epsilon. = the dielectric constant of the substrate (no
units).
In most practical applications, F, H, and .epsilon. are usually
given. As seen from equation (1), a closed form solution is not
possible for the square element. However, numerical solution can be
accomplished by using Newton's Method of Successive Approximation
(see U.S. National Bureau of Standards, Handbook of Mathematical
Functions, Applied Mathematics Series 55, Washington, D. C., GPO,
Nov. 1964) for solving equation (1). Equation (1) is obtained by
fitting curves to Sobol's equation (Sobol, H. "Extending IC
Technology to Microwave Equipment," ELECTRONICS, Vol. 40, No. 6,
Mar. 20, 1967, pages 112-124). The modification was needed to
account for end effects when the microstrip transmission line is
used as an antenna element. Sobol obtained his equation by fitting
curves to Wheeler's conformal mapping analysis (Wheeler, H.
"Transmission Line Properties of Parallel Strips Separated by a
Dielectric Sheet," IEEE TRANSACTIONS, Microwave Theory Technique,
Vol. MTT-13, No. 2, Mar. 1965, pp. 172-185).
RADIATION PATTERN
The radiation patterns for the E.sub..theta..sbsb.a field and the
E.sub..phi..sbsb.a field are usually power patterns, i.e.,
.vertline.E.sub..theta..sbsb.a.vertline..sup.2 and
.vertline.E.sub..phi..sbsb.a.vertline..sup.2, respectively.
The electric field for the corner fed dipole is given by ##EQU1##
and ##EQU2## where U = (U2-U3)/U5
T = (t3-t4)/t8
u2 = p sin (A .times. P/2) cos (k .times. A .times. sin .theta. sin
.phi./2)
U3 = k sin .theta. sin .phi. cos (A .times. P/2) sin (k .times. A
.times. sin .theta. sin .phi./2)
U5 = (p.sup.2 - k.sup.2 sin.sup.2 .theta. sin.sup.2 .phi.)
T3 = p sin (P .times. B/2) cos (k .times. B .times. cos
.theta./2)
T4 = k cos .theta. cos (P .times. B/2) sin (k .times. B .times.
.theta./2)
T8 = (p.sup.2 - k.sup.2 cos.sup.2 .theta.)
.lambda. = free space wave length (inches)
.lambda..sub.g = waveguide wavelength (inches) and .lambda..sub.g
.apprxeq.2 .times. A + (4 .times. H/.sqroot..epsilon.)
j = .sqroot.- 1
I.sub.m = maximum current (amps) ##EQU3## e = base of the natural
log r = the range between the antenna and an arbitrary point in
space (inches)
Z.sub.o = characteristic impedance of the element (ohms)
and Z.sub.o is given by ##EQU4## Therefore ##EQU5## and ##EQU6##
Since the gain of the antenna will be determined later, only
relative power amplitude as a function of the aspect angles is
necessary. Therefore, the above equations may be written as
and
The above equations for the radiation patterns are approximate
since they do not account for the ground plane effects. Instead, it
is assumed that the energy emanates from the center and radiates
into a hemisphere only. This assumption, although oversimplified,
facilitates the calculation of the remaining properties of the
antenna. However, a more accurate computation of the radiation
pattern can be made.
RADIATION RESISTANCE
Calculation of the radiation resistance entails calculating several
other properties of the antenna. To begin with, the time average
Poynting Vector is given by
where
* indicates the complex conjugate when used in the exponent
R.sub.e means the real part and
X indicates the vector cross product. ##EQU7## The radiation
intensity, K.sub.A, is the power per unit solid angle radiated in a
given direction and is given by
The radiated power, W, is given by ##EQU8## The radiation
resistance, R.sub.a.sbsb.a, is given by ##EQU9## where ##EQU10##
therefore ##EQU11##
Numerical integration of the above equation can be easily
accomplished using Simpson's Rule. The efficiency of the antenna
can be determined from the ratio of the Q (quality factor) due to
the radiation resistance and the Q due to all the losses in the
microstrip circuit. The Q due to the radiation resistance,
Q.sub.R.sbsb.a, is given by
where .omega. = 2.pi.F and L is the inductance of a parallel-plane
transmission line and can be found by using Maxwell's Emf equation,
where it can be shown that
and
the Q due to the radiation resistance, Q.sub.R.sbsb.a, is therefore
given by
The Q due to the copper losses, Q.sub.c.sbsb.a, is similarly
determined.
where R.sub.c.sbsb.a is the equivalent internal resistance of the
conductor. Since the ground plane and the element are made of
copper, the total internal resistance is twice R.sub.c.sbsb.a.
R.sub.c.sbsb.a is given by
where R.sub.s is the surface resistivity and is given by
where .sigma. is the conductivity in mho/in. for copper and .mu. is
the permeability in henry/in. .sigma. and .mu. are given by
Therefore, the Q is determined using the real part of the input
impedance
The loss due to the dielectric is usually specified as the loss
tangent, .delta.The Q, resulting from this loss, is given by
the total Q of the microstrip antenna is given by ##EQU12## The
efficiency of the microstrip antenna is given by
BANDWIDTH
The bandwidth of the microstrip antenna at the half power point is
given by
the foregoing calculations of Q hold if the height, H, of the
element above the ground plane is a small part of a waveguide
wavelength, .lambda..sub.g, where the waveguide wavelength is given
by
if H is a significant part of .lambda..sub.g.sbsb.a, a second mode
of radiation known as the monopole mode begins to add to the
microstrip mode of radiation. This additional radiation is not
undesirable but changes the values of the different antenna
parameters.
GAIN
The directive gain is usually defined (H. Jasik, ed., Antenna,
Engineering Handbook, New York McGraw-Hill Book Co., Inc., 1961, p.
3) as the ratio of the maximum radiation intensity in a given
direction to the total power radiated per 4.pi. steradians and is
given by
the maximum value of radiation intensity, K, occurs when 0 =
90.degree. and .phi. = 0.degree.. Evaluating K at these values of
.theta. and .phi., we have ##EQU13## since
Typical calculated directive gains are 2.69 db. The gain of the
antenna is given by
INPUT IMPEDANCE
To determine the input impedance at any point along the diagonally
fed microstrip antenna, the current distribution may be assumed to
be sinusoidal. Furthermore, at resonance the input reactance at
that point is zero. Therefore, the input resistance is given by
##EQU15## Where R.sub.t.sbsb.a is the equivalent resistance due to
the radiation resistance plus the total internal resistance or
The equivalent resistance due to the dielectric losses may be
neglected.
The foregoing equations have been developed to explain the
performance of the microstrip antenna radiators discussed herein
and are considered basic and of great importance to the design of
antennas in the future.
Antenna properties for the B mode can be determined in the same
manner as given above for determining the properties for the A mode
of oscillation. Since the A dimension equals the B dimension, the
values obtained for the A mode are equal in most cases.
Therefore:
Z.sub.o.sbsb.a = Z.sub.o.sbsb.b
R.sub.a.sbsb.a = R.sub.a.sbsb.b
Q.sub.r.sbsb.a = q.sub.r.sbsb.b
q.sub.c.sbsb.a Q.sub.c.sbsb.b
Q.sub.t.sbsb.a = q.sub.t.sbsb.b
.lambda..sub.g.sbsb.a = .lambda..sub.g.sbsb.b
G.sub.a = g.sub.b
r.sub.in.sbsb.a = R.sub.in.sbsb.b
R.sub.t.sbsb.a = R.sub.t.sbsb.b
Using the A mode equations for the B mode of oscillation saves
rederiving similar equations.
In evaluating the combined properties of the diagonally fed
antenna: ##EQU16## The combined gain is given by
the actual combined gain is normally evaluated at K.sub.max.sbsb.a,
.sbsb.b which turns out to be G.sub.(A) + G.sub.(B). The combined Q
is given by ##EQU17## and the combined radiation resistance is
given by ##EQU18##
If the B dimension is slightly smaller than the A dimension, a
phase difference occurs between the two modes of oscillation. This
can cause circular polarization to occur. This circular
polarization is desired in some applications, particularly when
this is obtainable with the use of a single coaxial-to-microstrip
adapter and no phase shifters. The most outstanding advantage of
the diagonally fed microstrip dipole, as compared to other
microstrip antennas is the ease in designing a singularly fed,
circularly polarized microstrip dipole antenna. FIGS. 8A and 8B
show a typical singularly fed, circularly polarized microstrip
dipole antenna. FIG. 9 shows a return loss versus frequency plot
for the circularly polarized antenna of FIGS. 8A and 8B. FIG. 9
shows a double resonance occurring at 2185 MHz and 2217 MHz. This
is due to the two modes of oscillation being present as mentioned
previously. FIGS. 10 and 11 show radiation plots for the XY plane
at 2185 MHz. Comparison of these two plots show that the
oscillation is predominant along the A dimension (1.72 inches).
FIG. 12 and FIG. 13 show radiation plots along both diagonals at
2185 MHz. The axial ratio at 2185 MHz was measured at 3 db. FIGS.
14 and 15 show radiation plots for the XY plane at 2217 MHz.
Comparison of these two plots show that the oscillation is
predominant along the B dimension (1.69 inches). FIGS. 16 and 17
show radiation plots along both diagonals at 2217 MHz. The axial
ratio at 2217 MHz was measured at 9 db. The axial ratio at 2200 MHz
was measured at 2 db.
The copper losses in the clad material determine how narrow the
element can be made. The length of the element determines the
resonant frequency of the antenna, as was mentioned in the
discussion earlier. It is preferred that both the length and the
width of the ground plane extend at least one wavelength (.lambda.)
in dimension beyond each edge of the element to minimize backlobe
radiation.
Typical antennas have been built using the above equations and the
calculated results are in good agreement with test results.
The near field radiation configuration, when the antenna is fed
along the diagonal of the antenna, is shown in FIG. 18. There are
two modes of current oscillation orthogonal to one another; the
current oscillation mode along the A dimension, and the current
oscillation mode along the B dimension. Depending on the input
impedance of each of these current modes, the field distribution
may change from diagonal fields, such as shown in FIG. 10, to
circulating fields (i.e., circular or elliptical).
When the microstrip antenna is fed along the diagonal, two modes of
oscillation can occur. If dimension A is equal to dimension B and
both are equal to the resonant length l for a specific frequency,
the oscillation along the A length (A mode) and the oscillation
along the B length (B mode) will have the same amplitude of
oscillation. In addition, the phase between the A mode of
oscillation will be equal to the B mode of oscillation. In such
case, the polarization is linear.
If dimension A is made slightly shorter than the resonant length l,
the input impedance for the A mode of oscillation will be
inductive. This inductive impedance will have a retarding effect on
the phase of the A mode of oscillation.
If dimension B is made slightly longer than the resonant length l,
the input impedance for the B mode of oscillation will be
capacitive. This capacitive impedance will have an advancing effect
on the phase of the B mode of oscillation.
By definition, circular polarization can be obtained if there are
two electric fields normal to one another, equal in amplitude and
having a phase difference of 90.degree..
In the case of the diagonally fed microstrip dipole antenna, there
is the A mode of oscillation and the B mode of oscillation creating
fields normal to one another. As previously mentioned, the phase of
one mode of oscillation can be advanced and the phase of another
retarded. If there is enough retardation and enough advance in the
fields, a 90.degree. phase can be obtained. The equal amplitude in
each of the fields can be obtained by coupling the same amount of
power into each mode of oscillation. This will provide circular
polarization.
Any variation of the phase of the above fields or its amplitude
will provide elliptical polarization (i.e., there must be some
phase difference, but not necessarily amplitude difference).
Elliptical polarization is the most general form of polarization.
Both circular and linear polarizations are special cases of
elliptical polarization. For linear polarization, only both phases
need to be equal.
Design equations for obtaining circular polarization in the
diagonally fed microstrip antenna can be obtained by using
transmission line theory. To begin with, the input impedance for an
open circuited transmission line is given by ##EQU19##
If both the A mode of oscillation and the B mode of oscillation are
analyzed, equation (1) can be rewritten for the A mode as ##EQU20##
and for the B mode as ##EQU21## where .alpha..sub.A and
.alpha..sub.B are propagation constants for the antenna circuit,
and ##EQU22##
where l is the resonant length for the frequency of interest. (It
is not necessary to have the actual element length A at resonance.
The element may be cut to a non-resonant length and made to
resonate with a reactive load.) If there is deviation from a square
element
since a closed form solution of l is not possible, numerical
solution can be accomplished by using Newton's Method of Successive
Approximation; when A and B dimensions are equal, then A = B = l.
If the A dimension is to be made slightly longer and the B
dimension is to be made slightly shorter:
and
At resonant frequency Bl = n.pi. where n = 1,2,3 . . . , and n
determines the order of oscillation. In this case, the order of
oscillation is the first order and Bl = .pi..
When the resonant waveguide length, l.sub.g, is made longer by
.DELTA.l.sub.A, then:
and ##EQU24## If n = 1, then ##EQU25## since l.sub.g = .lambda.g/2
##EQU26## Under these conditions ##EQU27## Equation (17) can be
written as ##EQU28## for moderately high Q antennas, the second
term in the numerator is small and may be neglected compared to the
other terms. Under these conditions
For circular polarization, the following two conditions must be
satisfied ##EQU37## and
as can be observed, determination of .DELTA.l.sub.A and
.DELTA.l.sub.B by manual computation is almost impossible. However,
the problem can be solvable by use of a computer. A further
reduction in the complexity of the problem is to assume
which is a good assumption when
.DELTA.l .sub.A << .lambda..sub.g/10
and
For these conditions
Therefore, ##EQU38## and ##EQU39##
The foregoing discussion involves a hypothetical case where the
feed point is located beyond the corner of the element at feed
point y.sub.H, as shown in FIG. 19.
Similar analysis is made for determining the conditions for
circular polarization at any feed point y.sub.F on the diagonal for
a typical diagonally fed antenna.
The diagonally fed electric microstrip dipole antenna can be fed at
the optimum feedpoint and also circular polarization can be
obtained using only a single feedpoint. This eliminates the need
for additional components that otherwise would be required for
circular polarization. Coaxial transmission lines, however, must be
used for arraying a plurality of these elements.
Obviously many modifications and variations of the present
invention are possible in the light of the above teachings. It is
therefore to be understood that within the scope of the appended
claims the invention may be practiced otherwise than as
specifically described.
* * * * *